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APPLICATION OF THE ANALYTICAL ELECTRONMICROSCOPE TO THE STUDY OF GRAIN

BOUNDARY CHEMISTRYE. Hall

To cite this version:E. Hall. APPLICATION OF THE ANALYTICAL ELECTRON MICROSCOPE TO THE STUDYOF GRAIN BOUNDARY CHEMISTRY. Journal de Physique Colloques, 1982, 43 (C6), pp.C6-239-C6-254. �10.1051/jphyscol:1982622�. �jpa-00222303�

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Colloque C6, supplément au n° 12, Tome 43, décembre 1982 page C6-239

APPLICATION OF THE ANALYTICAL ELECTRON MICROSCOPE TO THE STUDY OF GRAIN BOUNDARY CHEMISTRY

E. L. Hall

General Eleatrio Corporate Research and Development, P.O. Box 8, Soheneotady, New York 12301, U.S.A.

Résumé- La spectroscopie des rayons X avec haute définition de l'image employée dans un microscope électronique analytique (AEM) est une technique efficace pour étudier les changements chimiques aux joints de grains des métaux et des céramiques. Un avantage important est obtenu par l'emploi du microscope électronique analytique dans ces études: la capacité d'obtenir des analyses microchimiques quantitatives-—.. exactes des régions des joints de grains et de déterminer les caractéristiques struc­turales et cristallographiques des mêmes régions. Dans cet article les procédés expé­rimentaux de l'analyse AEM sont discutés, en particulier les avantages et les limita­tions de la technique. Deux cas très différents font exemple de la technique: la sé­grégation équilibre de Fe aux joints de grains de MgO (un effet coulombique) et l'é­puisement de Cr aux joints de grains de l'acier inoxydable causé par la précipitation des carbures enrichis en Cr. Un modèle mathématique nous permet de comprendre autant que possible les résultats expérimentaux pour chaque cas. L'effet des paramètres instrumentaux et structuraux sur les profils de composition des deux exemples est donné. On discutera tout au long les résultats donnés par l'analyse AEM et le rapport avec les théories du développement des variations chimiques aux joints des grains.

Abstract - High spatial resolution X-ray spectroscopy in the analytical electron microscope (AEM) is a powerful tool for the study of changes in chemistry which occur at grain boundaries in metals and ceramics. Two major advantages are realized through the use of the AEM in these studies: the ability to obtain accurate quantitative microchemical analysis of grain boundary regions, and the capability for determining the structural and crystallographic characteristics of the boundaries on which the chemical measurements were made. In this presentation, experimental procedures for AEM microanalysis are briefly discussed, with emphasis on the capabilities and limitations of the technique. The application of these procedures is illustrated using two important cases which serve to demonstrate a wide range of possible behavior: the equilibrium segregation of Fe to grain boundaries in MgO due to space-charge considerations, and the depletion of Cr at grain boundaries in stainless steel caused by the precipitation of Cr-rich carbides. A mathematical model will be utilized to extract the maximum information from the experimental data in each case. The effect of instrumental and structural parameters on the composition profiles in both systems will be shown. The types of information provided by the AEM, and its relation to theories of the development of chemistry variations at grain boundaries, will be discussed in detail.

1. Introduction

In recent years it has become well known that in multicomponent single-phase poly-crystalline materials, local variations in composition may occur at generalized high-angle grain boundaries. These variations may result from equilibrium or non-equilibrium processes, and may correspond to an enrichment (with the process described as segregation or precipitation) or depletion of a certain solute species in the grain boundary region. Chemistry changes at grain boundaries are extremely important phenomena since, while often occurring on a microscopic or atomic scale, they may influence or control the macroscopic properties of the material. For example, in ceramics, changes in grain boundary chemistry affect mechanical properties such as fracture strength, toughness, plastic deformation, and creep; electrical properties such as dielectric loss and conductivity; and other processes such as sintering, grain growth, and heterogeneous nucleation (1). In metals, grain boundary chemistry changes can cause embrittle-ment and loss of corrosion resistance, as well as have many other effects.

It is clear that a full understanding of structure-property relations in systems where grain

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1982622

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boundary chemistry changes have occurred requires a n accurate assessment of the magnitude and extent of compositional variation. In the past, a number of direct and indirect methods for studying grain kundary segregation have been utilized (for a review, see Gleiter and Chalmers (2)). These methods have generally suffered from the disadvantage that quantitative measure- ments were not possible on a scale similar t o that of the chemistry variation. More recently, the advent of analytical electron microscopy has provided the materials scientist with a new powerful tool for t h e study of grain boundaries. In t h e analytical electron microscope (AEM), a small probe of electrons, normally 0.5- 10 nm in diameter, is scanned across a specimen which is in the form of an electron-transparent thin foil. The transmitted electrons can be collected using a suitable detector to give a scanning transmission image on a cathode-ray tube. The microscope also has chemical analysis equipment such as an energy dispersive X-ray (EDX) detector andlor an electron energy-loss spectrometer, so tha t the elements present in the volume irradiated by t h e probe can be determined. In addition, the usual transmission electron microscope ITEM) operating modes a r e available in the AEM.

Several advantages are derived from the use of the AEM to study grain boundaries. Most importantly, quantitative high spatial resolution chemical information can be obtained from intact boundaries. From the same boundary, in the same microscope, high-resolution images and electron diffraction patterns can furnish structural and crystallographic information. Thus, structure-chemistry correlations can be obtained.

In the present paper, the experimental procedures for measuring chemical gradients a t grain boundaries using X-ray spectroscopy in the AEM will be briefly reviewed. The results of the application of these techniques will be presented for two systems: F e segregated to grain boundaries in MgO, and Cr-depletion a t grain boundaries in stainless steel. Methods for extracting the maximum information from the AEM data will be discussed. Finally, for both systems correlations will be described between the experimental results and the predicted behavior of the composition profiles from thermodynamic considerations. The relation of chemistry t o structure will be briefly considered.

I t should be mentioned for completeness that two other advanced analytical techniques have recently demonstrated considerable applicability to the study of grain boundary chemistry: Auger electron spectroscopy (3) and atom probe microscopy (4). In many ways these two techniques serve as complements t o the AEM technique. Auger electron spectroscopy requires the fracturing of the specimen along grain boundaries under ultra-high vacuum (often a difficult or impossible task) and hence crystalIographic and structural information concerning the grain boundary is lost. It also has relatively poor lateral spatial resolution and quantitation of data i s difficult. However, Auger spectroscopy has the advantage of excellent depth resolution, detectability of elements throughout the periodic table, and good elemental sensitivity for a segregated species. The atom probe, which couples a field-ion microscope with a time-of-flight mass spectrometer, provides atomic resolution images and chemical information, with straight- forward and accurate quantitation of the latter. I t may thus be the ultimate instrument t o study grain boundary chemistry and structure. However, i t is limited by an extremely small field of view, lengthy analysis time, and by problems with sample preparation and location of grain boundaries. The applicability of the atom probe t o non-metals has yet t o be convincingly demonstrated.

2. Technique

A. General

The physical layout and operating modes of the analytical electron microscope have been described previously (5,6). However, two points a r e worth mentioning here, since they critically impact the use of this instrument in the study of qrain boundary chemistry. First, the diameter of the incident probe of electrons used for microanalysis is related to the type of source employed. Three different types of electron sources a re currently in use: tungsten wire and LaB6 single crystals, both of which a r e thermionic emitters, and oriented tungsten used in a field emission mode. The smallest probe which can be produced by each of these sources is governed by the relationship

i a ~ d 8 / 3 (1)

where i is the current in t h e probe, d is the probe diameter, and B is the gun brightness. The probe diameter must be sufficiently large to provide suitable current for microanalysis. Each of the previously mentioned sources has a unique value for B, with LaB providipg $factor of 10 imorovement over heated tungsten and field emission tungsten a factor of 10 -10 . Thus, the field emission source allows the smallest probe size t o be used, but this particular emitter

r e w i r e s a n excellent vacuum (>l0-" torr) for reliable operation. The second consideration is t ha t t he energy dispersive X-ray detectors used for AEM

microanalysis cannot detect e lements of a tomic number <I1 due t o detector absorption of t h e low-energy X-rays from light elements. The technique of electron energy-loss spectroscopy (7,8,9) can provide chemical information for these elements, but this method is st i l l in t h e development stages and thus f a r has not been used t o investigate t h e composition of grain boundaries.

8. Microanalysis Procedures

The conventional methods of specimen preparation for transmission electron microscopy, which generally involve electropolishing of meta ls and ion milling of ceramics, are used t o prepare samples for AEM analysis. The resulting specimen has, in an idealized description, a wedge-shaped thin a rea eminating from the periphery of a hole. Grain boundaries fo r analysis must be oriented perfectly parallel t o the electron beam by tilting t h e specimen. The electron probe is stepped, either manually or controlled by automation, along a line perpendicular t o t h e boundary t o produce a composition profile across t h e boundary. The boundary should extend in a direction normal t o t h e edge of the foil, so tha t each s tep of t h e profile is taken a t an equal foil thickness. Finally, t h e boundary should be positioned along a line which i s parallel t o t h e l ine from the sample t o t h e X-ray detector, so tha t the X-rays a r e taken off parallel t o the boundary.

C. Ouantitation of X-ray Da ta

The X-ray intensities from each microanalysis point can be converted to composition using the formulas 110)

C~ I A = *AR and

where C A and CB a re t h e weight fractions of elements A and R, respectively, I and IB a re t h e X-ray intensities of these elements, and k is a constant. CR is t h e weight%raction of any remaining elements in t h e specimen. hel lac tor kAB does not vary with composition nor, t o a first approximation, with orientation. The absorption of X-rays may cause kAB to behave a s a function of thickness, and generally kAB is given by (1 1)

where kTF is t h e value for an infinitely thin foil ( / Ii i s t h e mass absorption coefficient of AR IJ % P ~ C element I In t h e specimen, a is the X-ray takeoff ang e, p is t h e density, and t is t he foil thickness. If i t is assumed t h a t t h e average depth of X-ray production is a t one-half of t h e foil thickness, eqn. 3 becomes (1 1 )

where R IJ

A AXB-A = [ ( -) 1 c s c a

SPEC p SPEC

I t is clear therefore tha t t he necessity for an absorption correction is d ic ta ted by t h e magnitude of the difference between the mass *orption coefficients of elements A and B i n t h e specimen. If th is difference is small, k - k and this value can be determined directly from s t a n d a f p or calculated from first prinA!3~ei (1 A? If AxB- is large, eqn. 3 must be used t o calculate k from t h e k value o 9 n e d using standards, an% this requires knowledge of t h e foil thicknesA;! t h e standah? Once k is known, eqns. 2 and 3 can be used t o calculate chemistry in the unknown. The foil thtclness must be measured a t each microanalysis point if absorption is important. Thickness can be measured in AEM specimens using convergent-beam electron

C6-242 JOURNAL DE PHYSIQUE

diffraction (13-15), contamination spot methods (161, thickness fringes, or projected widths of planar features (17).

D. Spatial Resolution

A critical parameter for the measurement of grain boundary chemistry using X-ray spectroscopy in the AEM is the spatial resolution for microanalysis, determined by t h e spatial extent of the beam in t h e specimen. This parameter is somewhat dependent upon t h e minimum incident probe diameter, discussed previously, but is generally dominated by the broadening of the electron beam in the specimen. This broadening is due t o elastic scattering, and i t s magnitude has been estimated using both Monte Carlo techniques and scattering models (for a review, see Newbury (18)). The single scattering model of Coldstein e t al. (11) provides a useful analytical expression which estimates the amount of broadening, b, of a point probe of electrons, namely

Z L )1/2 t3/2 cm b = 6 . 2 5 ~ 1 0 ~ ( - ( A (5) Eo

wher Z is the atomic number, E is the incident electron energy in eV, p is the density in g/cm3, A is the atomic weight, an& is the sample thickness in cm. Table I shows the values of broadening predicted by eqn. 5 and one of t h e Monte Carlo analyses (19); included in this table a r e values for MgO and stainless steel, which will be discussed in the subsequent section but for which no Monte Carlo data a re available. The single scattering model breaks down a t high atomic weights and large thicknesses, and so no values a r e indicated. Reasonable agreement is seen between t h e results of t h e simple scattering model and t h e more sophisticated Monte Carlo approach. For foil thicknesses typical of those encountered in AEM specimens (100-300 nm), i t is obvious that considerable broadening occurs compared with the incident probe diameter (1-10 nm). The total probe diameter, bT, and thus the expected spatial resolution for microanalysis is given by

where bo is the incident probe diameter.

Table I: Broadening, in nanometers, of a point probe of electrons as predicted by Eqn. 5 and by a Monte Carlo calculation (in parentheses). Eo = 100 kV.

Foil Thickness (nm)-. Material 10 50 I00 300 500

Carbon c 27 (16) 57 (33 MgO 0.27 3.0 8.4 44 94 Aluminum 0.26 (0.41) 2.9 (3.0) 8.1 (7.6) 42 (30) 91 (66) Stainless 0.61

Steel 6.8 19.3 101 216

Cold 1.6 (1.7) 17.3 (15) -- (52.2) -- (599) -- (1725)

3. Applications

The number of experimental systems in which X-ray spectroscopy in the AEM has been applied t o the study of grain boundary chemistry in a quantitative fashion is somewhat limited. As mentioned in the introduction, two investigations have been chosen, one from a metallic material and one from a ceramic, to illustrate the application of the technique and the resulting information provided. The chemistry variations in these two systems are caused by quite different mechanisms, and thus display very different properties. In this way, they serve t o illustrate a wide range of possible studies of this type.

At thermodynamic equilibrium, the surface and grain boundaries of an ionic ceramic material may carry an electric charge due t o the presence of excess ions of one type. This boundary potential is balanced bv an adjacent space charge cloud of opposite sign and equal magnitude. In pure materials, this charge arises from differences in the energy of formation of

anion versus cation vacancies. However, if aliovalent solute ions a re present, these will control the magnitude and sign of the boundary charge by affecting the vacancy concentrations. In the la t ter case, both the solute concentration and the temperature are important factors in determining the boundary potential. In doped oxide materials, this boundary potential is thought to be the major factor leading t o the segregation of solute ions t o the boundaries. The details of space-charge theory have been reviewed by Kingery (1).

In order t o examine the occurrence and magnitude of this type of segregation, samples of MgO doped with F e in the range 500-5000 cation fraction ppm were prepared using methods previously described (20). The sign of thg boundary charge in MgO is consistent with the segregation of a higher-valence ion (e.g., ~ e + ) t o the boundary.

Figure 1 shows a bright-field scanning transmission image of a typical boundary in a sample doped with 5360ppm F e which had been heat treated at llOoOc for 18 hours followed by air quenching. The boundary shows no indication of the presence of discrete precipitates or a segregated layer, and when oriented parallel t o the electron beam as in fig. 1, has a very narrow image width (-Snm). Figure 2 is the result of a composition profile across the boundary in fig. 1, given as weight fraction iron (CFe) versus distance from the grain boundary. It is d e a r that significant iron segregation has occurred to the boundary, and that the segregation extends less than lOnm into the matrix on either side of the boundary. The foil thickness in the boundary region analyzed was 119nm, measured using convergent beam electron diffraction. The approximate incident probe size was lnm, yielding from eqn. 6 a total probe diameter of 12nm. The effect of probe size on profiles such as fig. 2 will be considered subsequently.

Figure 1. Bright-field scanning trans- Figure 2. Iron composition profile across mission image of grain boundary in MgO. boundary in Fig. I. From ref. 22.

The effects of solute concentration and annealing temperature on the segregation of F e to boundaries in MgO a r e shown in figs. 3 and 4. In fig. 3, four profiles a re seen that were taken across grain boundaries in samples of MgO doped with different amounts of F e from 540 t o 5360ppm. The samples had been annealed a t 1 1 0 0 ~ ~ for 18 hours and then air quenched. The data illustrate that the amount of Fe present a t t h e grain boundaries increases with increasing d o ~ a n t level. However, the width of the segregated region is not a strong function of dopant level. A significant asymmetry is observed in several of t h e profiles, and this will be discussed subsequently. In fig. 4, the data for all of the boundaries examined a re presented as a plot of excess F e a t the grain boundaries, obtained from the area under the concentration profiles af ter the matrix level was subtracted, versus dopant level for three different heat treatments. The error bars represent the range of values found a t boundaries in each particular sample. The l a r g s t amount of s e g r ~ a t i o n was observed for specimens which had been slow-cooled (0.5 Clsecond) from 1500 C; much of this segregation undoubtably occurred during slow cooling. For the samples which had been air-quenched (300~C/second), larger amounts of segregation are seen for the sample aged a t 1 1 0 0 ~ ~ .

These results support several of the predictions of space-charge theory. For doped NaCI, which has the same sign for the boundary potential as MgO, Kliewer and Koehler (21) found that for a fixed solute concentration, both the magnitude of the potential and the width of the space charge region increase as the temperature is lo~ered ,~a l though the latter effgct is quite small. Thus, the larger amount of segregation found a t 1100 C compared with 1500 C could be due to the increased boundary charge. Further, they found that as the dopant level was increased a t a given temperature, the charge magnitude also increased. This is reflected in t h e data in fig. 3. The space charge width was predicted to decrease with increasing solute levels, and this is not

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Distance from grain boundary ( 8)

Figure 3. Iron composition profiles across boundaries in MgO doped with various levels of iron. From ref. 20.

Figure 4. (Right) Excess iron concentra- tion a t grain boundaries versus dopant level in MgO for various heat treat- ments. From ref. 20.

-

Sbw cooled fmm 1500°C - 0 Air quenched from1 100°C 0 Air quenched f r m 1500DC

0 0.005 0.010 0.015 Nominal C F ~

seen in fig. 3. However, the magnitude of this decrease is a few nanometers and thus is probably below the spatial resolution of the microanalysis.

One extremely important consideration for obtaining the maximum information from profiles of the type shown in fig. 2 is the effect of the probe size, which is a function of foil thickness. The geometry associated with the physical process is shown schematically in fig. 5. I t is clear that as the foil thickness increases and the probe broadening increases, a marked effect may be seen in the composition profile data. The influence of foil thickness in t h e MgO system has been examined using both experimental and theoretical approaches (22). Figure 6 shows the superposition of five profiles across the same boundary a t different foil thicknesses for t h e Fe- doped MgO sample from which figs. 1 and 2 were taken. The thickness and value of b from eqn. 5 for each profile are also given. The results reveal that increasing foil thickness does not cause

an appreciable broadening of the composition profile, but does strongly affect the value of CFe measured a t t h e boundary. An analytical model was constructed in an attempt t o analyze this result and study the effect of various parameters. In this model, the true concentration profile is represented as a Gaussian of height Co and half-width a. The electron beam is likewise

ELECTRON BEAM

4 0.07

X / \ T o.-

i 0.05

0.04

CF. Figure 5. Schematic representation of electron beam geometry in thin foil. "03

From ref. 22. 0.02

Figure 6. (Right) Experimental results 0.0'

of iron concentration profiles across a single boundary a t various foil thick- 1 nesses. From ref. 22. &, i0 do 40 30 20 10 o $0 20 30 50 70 80

Distmna ~ m m Onin w n d 8 w (nm)

2 described as a Gaussian of height equal to n/n [p(z) ] and half-width p(z), where n is the total number of incident electrons and p ( ~ ) is the probe half-width a t any depth z below the foil surface. At the foil exit surface Z=t and p(t) = bT/2, using eqn. 5 to describe t h e beam broadening. The convolution of the two Gaussians gives the X-ray intensity which is experimentally measured. It is possible t o show that this convolution results in a measured solute concentration a t a distance X frod the boundary (fig. 5) given by Co F (X)/t, where

The results of the application of this model t o t h e case of F e in MgO are shown in fig. 7. For fig. 7a, exoerimental parameters were chosen to match the situation in fig. 6. The true concentration profile is indicated by the dashed curve, with a half-width of 2.5nm. The incident probe diameter was chosen t o be Inm. The model accurately predicts the behavior of the experimental data in a qualitative fashion; namely, a t each foil thickness, t h e measured profiles accurately indicate the width of the true profile, but the level of segregation measured a t the boundary decreases ap~reciably as the foil thickness increases. Therefore, the analytical model, although simple, adequately describes the physical situation. More sophisticated Monte Carlo- type analyses have been carried out for t h e data in fig. 6 (23,241, and good agreement is seen with the model. The model can be used t o show that whenever the total probe diameter is significantly larger than the full width a t half maximum of the concentration profile, a large effect of specimen thickness is seen. This effect results in erroneous values for the amount of segregant a t the boundary, but the width of t h e boundary layer is accurately determined except in extreme cases. However, a much stronger dependence of the results on initial probe size than expected is predicted. Figure 7b shows the measured composition profiles predicted for t h e true profile from fig. 7 a if a 10 nm incident probe is used. The F e segregation is barely visible and bears lit t le resemblance t o the true profile. Thus, i t appears that significant benefit may occur from the use of a field-emission gun AEM (incident probe size = -1nm) rather than a thermionic-emission AEM (incident probe size = -10 nm) t o study equilibrium segregation.

O 15 10 5 0 5 10 15 Distonce from groln boundary (nm)

0.9

0.8

, 0.7 u -. 5 0.6 - p 0.5

0.4 u"

0.3

0.2

0.1

O 15 10 5 0 5 10 15 D~stance from graln boundary (nm)

Figure 7. Calculated results from model of experimental profiles a t various foil thicknesses (solid curves) for true profile as shown (dashed curve), for incident probe sizes of (a) I nm and (b) 10 nm. From ref. 22.

Application of the model t o the data in fig. 6 indicates that 9-14 weight percent F e is Dresent a t the grain boundary studied. However, comparison of figs. 6 and 7 shows that there is rather poor quantitative agreement between the model and the experimental results a t large foil thicknesses. This is undoubtablv due t o both uncertainty in several of the experimental oarameters, and the fact that the t rue profile is most likely not a Gaussian function. Clearly, additional information concernine, the true profile configuration is needed for accurate quantita- tive analysis. However, the AEM data is in excellent agreement with Auger studies which indicate that F e (25) and impurities such as Ca, Si, and Ti (261, when segregated to grain boundaries in MgO, extended less than 5-10 atomic layers into t h e matrix.

The results in figs. 3 and 4 appear t o show that the boundary potential is the dominant factor in controllinq the segregation of iron t o grain boundaries in MgO. However, other driving forces for equilibrium segregation, e.g., interfacial energy effects, which a re poorly understood

C6-246 JOURNAL DE PHYSIQUE

in ceramics, cannot be ruled out on the basis of this evidence. I t is unlikely that strain energy effects play a role, since these ~ f f e c t s are weak for t h e ~ e * ) ion in MgO. Ion microprobe experiments (27) showed tha t ~ e + ions did not segregate t o MgO grain boundaries, as would be e x ~ c t e d if the boundary potential were t h e principle factor. Final&, i t has been shown tha t Sc ions, which have a nearly identical ionic radius t o tha t of Mg , segregated strongly t o boundaries in MgO (28). I t must be emphasized, however, tha t t h e data in figs. 3 and 4 a re intended t o represent observed trends. Insufficient numbers of boundaries were analyzed t o yield statistically meaningful results, and no at tempt was made in these data t o take into account probe size/sample thickness considerations as discussed in the previous paragraphs.

Some effect of the nature of the individual boundary on the magnitude of the F e segregation was seen in the MgO study. For example, in samples doped with 5360ppm F e and annealed a t 1100 C for 18 hours followed by air quenching, data from several boundaries in thin regions of t h e foil ( SOnm), where probe broadening effects will be small, showed variation from 5-8 weight percent iron. Multiple measurements on individual boundaries demonstrated tha t this could not be associated with instrumental parameters, and thus represented a real variation. I t is well known that the nature of the individual grain boundary, specified by t h e grain misorientation and boundary orientation, can affect such processes as heterogeneous precipita- tion and grain boundary migration. In t h e case of F e in MgO, i t appears that equilibrium segregation can also be affected by grain boundary structure, although equilibrium segregation theory, including space-charge considerations, does not take this into account. Similar boundary- to-boundary variations in the amount of impurities such as antimony and phosphorus, which segregate by a n equilibrium mechanism t o grain boundaries in low-alloy steels, have been observed using Auger electron spectroscopy (29). In tha t work, variations of 230% about a mean value were seen at equilibrium.

A final point which should be discussed is t h e occurrence of asymmetries in the composition profiles across the grain boundaries in MgO (fig. 3). These asymmetries a r e frequently observed, and three mechanisms a re possible as explanations: (1) instrumental effects; (2) a t rue physical asymmetry resulting from different iron diffusion paths t o the grain boundary due t o t h e crystallography of t h e two grains which make up t h e boundary o r due t o asymmetry of the space charge; and (3) boundary movement during segregation. The possibility of instrumental effects such a s boundary inclination or diffracting condition introducing a n asymmetry into t h e profiles was investigated by tilting the specimen, which did not effect t h e profiles. However, it has recently been pointed out (30) that under certain circumstances the electron beam shape i s such that an asymmetric profile of the type shown in fig. 3 could result. Consideration of the second possibility would require a detailed analysis of t h e crystallography of t h e grain boundary and i t s effect on diffusion or space charge, which was not done in the MgO study. Finally, solute drag by a moving boundary which had a layer of segregant present would be expected t o produce profiles identical t o those seen in the MgO case. Recent work on segregation in MgO (31) has seen considerable correlation between asymmetric segregant profiles and abnormal grain growth, with the asymmetry consistent with boundary migration toward t h e center of curvature. I t is clear that additional work is necessary t o fully understand the compositional asymmetries in MgO.

B. Sensitized Stainless Steel

A second application which will be discussed involves chromium depletion at grair boundaries in sensitized stainless steel. Although this is a very different situation compared witb the MgO study since the chemistry change occurs 'due t o a non-equilibrium mechanism, the analysis methods a r e identical and certain aspects of the results a r e similar. The term sensitization refers t o t h e breakdown of the corrosion resistance of stainless steels which hac been slowly cooled from a solutionizing temperature or isothermally heated in t h e temperature range 550-800'~. The corrosion susceptibility is associated with grain boundaries, and i s cause by the precipitation of Cr-rich MZ3C6 carbides along the boundaries. This depletes t h e matri and grain boundary regions adjacent t o t h e carbides of Cr, t h e key element in t h e corrosio resistance of these steels, and leads to intergranular corrosion. The exact magnitude and widt of the Cr-depleted regions is of great importance t o t h e understanding of the corrosio properties of these materials.

Samples of 316LN (nuclear grade) stainless steel, which contains 16 w/o Cr, 10 w/o Ni, w/o Mo, 0.02 w/o C,, and 0.06-0.16 N, were examined in the sensitized state, as determined macroscopic corrgslon tests. An example of the results is shown in fig. 8, from a

i sensitized a t 650 C for 100 hours. Figure 8a displays a boundary in this sample with carbides present, where the M portion consists of 64 w/o Cr , 3 w/o Ni, 14 w/o Mo and 19 At the boundary adjacent t o the carbides, in the location indicated by the line, the profile in f i 8b was obtained. I t can be seen that significant Cr-depletion is present, and that Mo

0 I I I I I I I , , -1OW -800 -600 -400 -200 0 200 400 600 800 low

DISTANCE FROM GRAIN BOUNDARY, nm

700/300

13

12

-800 -600 -400 -200 ii DISTANCE FROM GRAIN BOUNDARY, nrn

Figure 8. (Left) (a) Bright-field trans- mission image of grain boundary in stain- less steel. (b) Composition profile a t location indicated by line in (a).

Figure 9. (Above) Effect of sensitization temperature and time on chromium pro- files across boundaries in the vicinity of carbides.

been depleted by the growing carbide. The full width a t half maximum of the profile is "80 nm, and the Cr level a t the boundary is 12.6 w/o. The effect of both annealing t e m e r a t u r e and time is iuustrated by the chromigm profiles in fig. 9, from samples annealed a t 600 C for 100 hours, 650 C for 50 hours, and 700 C for 100 and 300 hours, which can be compared with fig. 8. With the exception of 600 C for 100 hours, all of these specimens were sensitized. I t can be seen that the early stages of sensitization correspond t o an increasing depletion of Cr in the vicinity of the carbide. At the onset of precipitation, the minimum Cr concentration a t equilibrium with the carbide occurs a t the carbide-matrix interface. With time, the Cr-depletion extends along the boundary, with this process controlled by Cr diffusion. The progress of this process is reflected in the 600/100 and 650150 profiles. After a certain time, the equilibrium C r level is measured by the AEM profiles, and annealing for longer times simply causes an increase in the width of the depleted region. Measurement of the Cr level near carbides a t many boundaries in samples annealed a t 7 0 0 ' ~ for 100 and 300 hours indicated that t h e equilibrium Cr value was 12.13.5. These results can be compared with thermodynamic models of the sensitization process (32,331. Goodl$greement is seen with predictions of the width of the depleted zone, 1, which is equal to (4Dt) , where D is the diffusivity of Cr in the matgx and t is the annealing time. However, the Cr content in equilibrium with the carbide a t 700 C is calculated to be 17.9 a/o ("16.8 w/o). This discrepancy may be due t o the fact that the effect of elements such as Mo and N on the Cr and C activity coefficients were not taken into account.

The effect of probe size and beam broadening on t h e non-equilibrium segregation profiles in figs. 8 and 9 is considerably less than for MgO due t o the large width of the Cr-depleted region. This is illustrated in fig. 10, in which the convolution model previously described was applied to s ta in l~ss steel. In fig. 10a, the data points from the profile in fig. 9 corresponding to annealing a t 700 C for 100 hours are shown as X's, and a Gaussian is fit t o this data and labelled bo = 10 nm, the incident probe size. A profile representing the true Cr depletion can be derived from this and from knowledge of the foil thickness (214 nm from convergent beam electron diffraction). I t can be seen that there is very litt le difference between the experimental and true curves. The predicted effect of lar e r incident probe sizes (30 and 50 nm) is also shown, and this result indicates that for analyses of this type, a large probe with ample current (eqn. 1) is preferred. Finally, fig. lob demonstrates the effect of foil thickness on the experimental data

C6-248 JOURNAL DE PHYSIQUE

Figure 10a. Effect of inci- dent probe size (bo) on chromium depletion pr+ files in stainless steel. True profile is derived from experimental data (bo=lOnm).

I \--b,- 10 nrn I I I I I ~ ~ I ~ ~ I ~ J

-300 -250 -100 -150 -100 -50 0 50 100 150 200 250 300 DISTANCE FROM ORAIN BOUNDIRY. (nm)

Figure lob. Effect of foil thickness on measured results from true profile derived in fig. 10a.

-300 -250 -2W -150 -100 -50 0 50 100 150 200 250 300

B s h tan Oram Boundary. nrn

from a true profile such a s tha t shown in fig. 10a, and a very minor effect is seen in t h e thickness range (100-300 nm) typical of AEM specimens. Thus, AEM da ta from this type of non-equilibrium profile can be used directly without correction, and data from different boundaries in t h e same specimen may be compared directly.

Rather large asymmetries a r e frequently observed in t h e Cr-depletion profiles in stainless steel, and an example is shown in fig. Ilb, taken across the boundary in fig. Ila a t the location indicated by lineoA. Line B corresponds t o t h e location of the profile in fig. 9 from the sample annealed at 700 C for 100 hours, which i s not asymmetric. For asymmetries of t h e magnitude seen in fig. 11, instrumental effects can be ruled out. As further evidence, inspection of fig. Ila reveals that some preferential thinning during specimen preparation has occurred at t h e boundary due t o the depletion of chromium, and this preferential thinning is also asymmetric and matches the Cr-depletion profile. In every case examined, t h e asymmetries were observed a t boundaries which have noticeable curvature, and the degree of curvature was somewhat related t o t h e magnitude of t h e asymmetry. This supports the view tha t the asymmetries develop due to boundary migration. The long asymmetric tail always occurred, however, ahead of the boundary if migration toward the center of curvature is assumed. In diffusion-induced grain boundary migration, boundaries a re seen to migrate against their curvature (35). It can also be noted (fig. Ila) tha t the carbides in t h e vicinity of t h e asymmetric profiles are growing preferentially into the grain corresponding t o the long depletion tail, and hence the nature of the carbide-matrix interface may play a role in developing these asymmetries. Clearly, asymmetries of this type can play an important role in the corrosion behavior of the steel, and more study is warranted.

4. Summary

The applications of X-ray spectroscopy in t h e analytical electron microscope t o t h e study

Figure Ila. Bright-field transmission Figure Ilb. Composition profile a t loca- image of grain boundary in stainless tion indicated by line A in (a). steel.

of grain boundary chemistry discussed in this paper illustrate the usefulness of this technique for both equilibrium and nokequilibrium composition variations. With careful assessment of experimental conditions, i t seems likely that very high quality quantitative microanalysis can be performed with excellent spatial resolution. A large number of additional studies using this technique could be envisioned which would provide important information related t o t h e microscopic and macroscopic behavior of materials. For example, Cahn, Pan and Balluffi (35) have used the AEM t o study diffusion-induced grain boundary migration in specially-prepared bicrystals. Briceno-Valero and Gronsky (36) have recently measured a periodicity in zinc concentration along special boundaries in A1 bicrystals which appears t o correlate with a structural periodicity in the boundary. The entire area of grain boundary structure-grain boundary chemistry interrelation appears t o be directly approachable using a combination of X- ray spectroscopy and high-resolution imaging in the AEM. Thus, the AEM can be demonstrated t o be an important tool in the study of grain boundary structure and properties.

5. Acknowledgments

The author would like t o acknowledge t h e contributions of t h e following people t o t h e work discussed in this paper: Dr. T. Mitamura, Prof. W.D. Kingery, and Prof. J.B. Vander Sande, Massachusetts Institute of Technology, Cambridge, MA, who provided samples, helpful dis- cussions, and financial support for the MgO work; Dr. D. Imeson, Massachusetts Institute of Technology, who developed the probe convolution model; and Drs. C.L. Briant, R.A. Mulford, and Ms. Y.M. Kouh, General Electric Corporate Research and Development, Schenectady, NY who provided samples, insight and technical assistanc6 for t h e stainless steel research. Partial support was provided by an IBM Postdoctoral Fellowship and by t h e Electric Power Research Institute, Contract No. RP-968- I.

References

1. KINGERY, W.D., J. Amer. Ceram. Soc. 57 (1974) 1, 74. 2. GLEITER, H. and CHALMERS, B., High-Angle Grain Boundaries (Pergamon Press, Oxford)

1972. 3. STEIN, D.F., JOHNSON, W.C. and WHITE, C.L., Grain Boundary Structure and Properties,

G.A. Chadwick and D.A. Smith, eds. (Academic Press, London) 1976, p. 301. 4, SMITH, G.D.W., GARRATT-REED, A.J., and VANDER SANDE, J.B., Quantitative Mi-

croanalysis With High Spatial Resolution (The Metals Society, London) 1981, p. 238. 5. WILLIAMS, D.B., and EDINGTON, J.W., Norelco Reporter, 3 (1981) 2 (available from

Philips Electronic Instruments Inc., Mahwah, NJ, USA 07430). 6. VANDER SANDE, J.B. and HALL, E.L., J. Amer. Ceram. Soc. 61 (1979) 246. 7. ISAACSON, M. and JOHNSON, D., Ultramicroscopy L(I975) 33:

C6-250 JOURNAL DE PHYSIQUE

JOY, D.C., Introduction To Analytical Electron Microscopy, J.J. Hren, J.I. Goldstein, and D.C. Joy, eds. (Plenum Press, NY) 1979, p. 223. MAHER, D.M., ibid, p. 259. CLIFF, G. and LORIMER, G.W., J. Micros. 103 (1975) 203. GOLDSTEIN, J.I., COSTLEY, J.L., LORIMER, G.W., and REED, S.J.B., Proc. SEM (IITRI, Chicago) 1977. D. 315. GOLDSTEIN, 'J.I., Introduction t o Analytical Electron Microscopy, J.J. Hren, J.I. Gold- stein. and D.C. Jov. eds. (Plenum Press. NY) 1979. D. 83. KELLEY, P.M., ~OSTONS, A., BLAKE, R.G., a& NAPIER, J.G., P ~ Y S . Stat. SOL (a) 2 (1975) 771. ALLEN, S.M., Phil. Mag. A, e ( 1 9 8 1 ) 325. ALLEN, S.M. and HALL, E.L., accepted for publication, Phil. Mag. RAE, D.A., SCOTT, V.D., and LOVE, G., Quantitative Microanalysis With High Spatial Resolution (The Metals Society, London) 1981, p. 57. HALL, E.L. and VANDER SANDE, J.B., Phil. Mag. 532 (1975) 1289. NEWBURY, D.E., Microbeam Analysis-1982, K.F.J. Heinrich, ed. (San Francisco Press, Inc., San Francisco) 1982, p. 79. NEWBURY, D.E. and MYKLEBUST, R.L., Ultramicroscopy 3 (1979) 391. MITAMURA, T., HALL, E.L., KINGERY, W.D., and VANDER SANDE, J.B., Ceram. Inter. 5 (1979) 131. KLIEWER, K.L. and KOEHLER, J.S., Phys. Rev. A. 140 (1965) 1226. HALL, E.L., IMESON, D., and VANDER SANDE, J.B., Phil. Mag. A 9 (1981) 1569. NEWBURY, D.E. and MYKLEBUST, R.L., Microbeam Analysis-1980, D.B. Wittry, ed., (San Francisco Press, Inc., San Francisco) 1980,173. TWIGG, M.E., LORETTO, M.H., and FRASER, H.L., Phil. Mag. A 2 (1981) 1587. KfNGERY, W.D., Massachusetts Institute of Technology, Cambridge, MA, private commun- ication. JOHNSON, W.C., STEIN, D.F., and RICE, R.W., Grain Boundaries in Engineering Materials, J.L. Walter, J.H. Westbrook, and D.A. Woodford, eds. (Claitor's, Baton Rouge) 1975, p. 261. BLACK. J.R.H. and KINGERY. W.D.. J. Amer. Ceram. Soc. 62 (1979) 176. VANDER SANDE, J.B. and GARRATT-REED, A.J., proceedin& of the Thirty-Eighth Annual Meeting of the Electron Microscopy Society of America, G.W. Bailey, ed. (Claitor's, Baton Rouae) 1980. D. 102. BRfANT, E.L., accepted for publication, A d a Met. CLIFF, G. and KENWAY, P.B. Microbeam Analysis-1982, K.F.J. Heinrich, ed. (San Francisco Press, Inc., San Francisco) 1982, p. 107. CHANG, Y., Massachusetts Institute of Technology, Cambridge, MA, private communi- cation. STAWSTROM, C. and HILLERT, M., J. Iron and Steel Inst. 207 (1969) 77. TEDMON, C.S., VERMILYEA, D.A. and ROSOLOWSKI, J.H., 3. Electrochem. Soc. (1971) 197- HALL, E.L., Proceedings of the Fortieth Annual Meeting of the Electron Microscopy Society of America, G.W. Bailey, ed. (Claitor's, Baton Rouge) 1982, p. 519. CAHN, J.W., PAN, J.D. and BALLUFFI, R.W., Scripta Met. 13 (1979) 503. BRICENO-VALERO, 3. and GRONSKY, R., Proceedings of t h e Thiry-Eighth Annual Meeting of the Electron Microscopy Society of America, G.W. Bailey, ed. (Claitor's, Baton Rouge) 1980, p. 360.

D I S C U S S I O N

D. WOLF : 1. I don't see why you need t h e space charge around the boundary

a t a l l t o explain the f a c t t h a t ~ e 3 + ions segregate t o the boun-

dary.Wouldntt it be s u f f i c i e n t t o pos tu la te a binding of the

impurity t o the surface thus es tab l i sh ing a chemical p o t e n t i e l

gradient a s the d r iv ing force?

2. How have you determined the f a c t t h a t the boundary was nega-

t i v e l y charged? Do you have a microscopic explanation f o r t h i s

negative charge?

E.O. HALL : The r e s u l t s on MgO presented i n my paper a r e simply cons i s ten t

with the predict ions of space-charge theory ; they do not prove

t h a t t h i s mechanism is s o l e l y responsible f o r Fe segregation i n

t h i s system. The s trong binding of i sova len t and a l iova len t

dopants t o g ra in boundaries and surfaces i n MgO, presented by

you i n t h i s conference is a possible a l t e r n a t i v e mechanism. This

l a t t e r mechanism explains q u i t e well the observed segregat ion

of impuri t ies such a s S i and Ca t o the boundaries i n MgO(20).

However, Black and Kingery (27) found t h a t i sova len t cat ions

( ~ e + 2 , SC'~) did not segregate t o surfaces i n MgO, suggesting

t h a t a space-charge component must be dominant f o r these elements.

The negative charge on t h e boundary can be postulated using

an argument s imi la r t o t h a t of Kliewer and Koehler (21) f o r

NaC1, based on the concentration of anion and ca t ion vacancies

a t thermal equilibrum. The microscopic mechanism involves vacancy

annih i la t ion a t defects such a s g ra in boundaries and dislocation$.

However, t h i s charge has not been d i r e c t l y measured, and i t s

exis tence i s simply i n f e r r e d from the bas ic concepts and experi-

ments such as our own.

V. VITEK : Why do you think t h a t an i n t r i n s i c asymmetry of the boundary

s t r u c t u r e i s the l e a s t l i k e l y reason f o r the asymmetry of the

segregation p r o f i l e ? Almost a l l boundaries a r e asymmetric, sym-

metr ical twins a r e ra ther spec ia l .

E.O. HALL : The s t r u c t u r e asymmetry associated with a generalized gra in

boundary i s local ized t o a region t h a t i s only a few atom layers

wide a t t h e boundary. Therefore, the asymmetries i n MgO, which

extend a t l e a s t 20nm from the boundary, a r e d i f f i c u l t t o r e l a t e

JOURNAL DE PHYSIQUE

t o the s t r u c t u r a l asymmetry. The experimental evidence c l e a r l y

suggestsboundary movement a s the dominant fac tor . Certainly, i n

s t a i n l e s s s t e e l , where asymmetries which extend severa l microns

i n t o the grains have been observed, boundary s t r u c t u r e can play

no ro le .

L. HOBBS : I have two comments :

1. One must be ca re fu l t o assigne a cen te r of curvature t o a

boundary surface based s o l e l y on the l i n e curvature of i t s in te r -

sec t ion with a t h i n f o i l . It is possible t h a t i n th ree dimensions

the ac tua l cen te r of curvature l i e s on t h e opposite s i d e of t h a t

deduced from TEM, and t h i s information is not read i ly ava i lab le i n

most TEM experiments unless p r i o r examination of t h e boundary on

bulk i s p rac t icab le .

2. You have ind ica te t h a t your r e s u l t s on Fe segregat ion i n MgO

a r e consis tent with a 3-5 nm space charge region of moderate

segregation, but equal ly well with a highly segregated (2% wlo)

Inm slab. This a l s o implies t h a t a monolayer s l a b of 100% Fe

should give s imi la r r e s u l t s . Given the s p a t i a l reso lu t ion res-

t r i c t i o n s f o r AEM, i s i ts r e a l l y possible to say anything more

about the s t r u c t u r e of segregat ion than t h a t segregation is pre-

sen t?

E.O. HALL : With regard t o your comments :

1. Your f i r s t comment i s of course cor rec t and should be careful-

l y considered when boundaries a r e s tudied i n t h i n f o i l s . I w i l l

only add a s a po in t of c l a r i f i c a t i o n t o the t e x t t h a t i n the re-

cent work on asymmetric boundaries i n MgO (31) which cor re la ted

the asymmetry with boundaries moving toward t h e i r center of c u r

vature, the curvature was measured using o p t i c a l microscopy

p r i o r t o ana lys i s i n the AEM.

2. Comparison of f i g s . 6 and 7a i n the t e x t would ind ica te t h a t ,

based on a Gaussian d i s t r i b u t i o n with a half-width of 5nm, a

concentration of 9.5w/o i s present a t the boundary. Application

of a simple geometrical model shows t h a t i f the d i s t r i b u t i o n i s

instead approximated a s a s lab lnm thick, the g r a i n boundary con-

cen t ra t ion is % 25 w/o; a s l a b 3nm th ick ( the predicted width of

the space charge region a t llOO°C) would give a near ly i d e n t i c a l

r e s u l t t o the Gaussian model ; and a monolayer s l a b (width = 0.4nd

would y ie ld a value of 57 wlo. Therefore, i t i s c l e a r t h a t some

additional information is necessary concerning the exact shape and

extent of the segregation if very accurate value of the amount of

segregant is to be obtained. This is an exemple of how a technique

such as Auger electron spectroscopy, which has excellent depth re-

solution, could be used to complement the U M study and provide

this information. In any case, application of the various models

should only be expected to yield an "order of magnitude" type of

value for the grain boundary segregation.

P. GUIRALDENQ : 1. Vous avez note une asymdtrie dans les profils de d6chromisation

au voisinage des carbures M23C6 pr6cipit6s dans l'acier inoxydable

austdnitique : j e pense que celle-ci peut Gtre due au caractsre

cohbrent ou incoh6rent de la croissance de ces derniers, la prb-

sence d'uneinterface incohgrente matricelcarbure dans certaines

rdgions Stant probablement la preuve d'dchanges atomiques plus

importants et d'une ddchromisation plus forte du c6t6 dela matrice

que dans une zone opposbe, pour le m6me carbure, oii il y a eu

effet d'bpitaxie.

2. Vous avez prouvd qu'au voisinage de joints d'acier inoxydable

NiCrMo fortement allid , dans des zones 01: il n'y a pas prbcipi-

tation de carbures, il y a aussi ddchromisation et migration du

joint lors du traitement thermique. Ceci montre bien qu'il faut

Btre tras prudent dans le choix d'un coefficient de diffusion en

volume Dv, si l'on veut mesurer un coefficient de diffusion inter-

granulaire, ou plut6t une diffusivitg intergranulaire PJ, puisque

le volume au voisinage du joint est en fait non homogsne et carac-

t6risE par un gradient chimique en chrome ddcroissant vers le

joint et par un gradient chimique en nickel croissant, de faqon - compldmentaire .

J.Y. LAVAL : I would like to make a comment to try to complete your informa-

tions concerning analytical electron microscopy. Grain boundaries

data have indeed already been obtained by electron energy loss.

In that field I think it would be fair to mention the results

obtained in Orsay by Colliex and al. on their V. G. microscope

equipped with a very efficient detector. I would like to mention :

I . The detection of oxygen precipitation (100 atoms) along dislo-

cations in germanium G.B. (Colliex and Bourret, 82) correlated

with high resolution studies.

JOURNAL DE PHYSIQUE

2. The detection of a different EXELFS structure for oxygen in

the matrix and at the grain boundary on silicon nitrides (Trebbia

Colliex and Laval, 82). This technique gives new insights into the

bondings at grain boundaries and will be particularly useful for

analyzing interfaces such as metal-oxide for instance.

E.O. HALL : I think it would be fair too to mention that the spatial resolu-

tion is better with electron energy loss than with X-ray.